A Selection of Applied Mathematics Problems

1988 ◽  
pp. 128-138
Author(s):  
Avner Friedman
Keyword(s):  
Applied Mathematics ◽  
Mathematics Problems ◽  
Selection Of

XX.—Studies in Practical Mathematics. II. The Evaluation of the Latent Roots and Latent Vectors of a Matrix

1938 ◽  
Vol 57 ◽  
pp. 269-304 ◽  
Author(s):  
A. C. Aitken
Keyword(s):  
Applied Mathematics ◽  
Dynamical Theory ◽  
Mathematics Problems ◽  
Principal Axes ◽  
Practical Mathematics ◽  
Latent Roots

In many branches of applied mathematics problems arise which require for their solution a knowledge of the latent roots of a matrix A, sometimes only the root of greatest modulus but often the second and other roots as well, and the corresponding latent vectors. A few examples, among many that might be cited, are problems in the dynamical theory of oscillations, problems of conditioned maxima and minima, problems of correlation between statistical variables, the determination of the principal axes of quadrics, and the solution of differential or other operational equations. It is important, therefore, to have a choice of methods for obtaining latent roots and latent vectors without undue labour, and the object of the present paper is to augment the existing store of such methods.

scholarly journals A MATHEMATICAL MODEL FOR SUMMING ROTARY MOTIONS

2020 ◽  
pp. 32-45
Author(s):  
Igor' Popov ◽  
Keyword(s):  
Applied Mathematics ◽  
Analytical Description ◽  
Practical Aspect ◽  
Straight Line Segment ◽  
Planetary Gears ◽  
Mathematics Problems ◽  
Straight Line ◽  
Automation And Control ◽  
Rotational Motions ◽  
And Control

In this work, using the means of applied mathematics, problems are solved related to the field of automation and control of technological processes, namely, the analytical description of superpositions of rotations that occur during the operation of numerous mechanisms. The practical aspect of the topic is determined by the fact that in mechanisms such as planetary gears, cutter drives in machines for cleaning pipes of large diameters, etc. summation of rotational motions is realized, and the shape of the hodograph is useful information in the design of such devices. The prerequisite for consideration is the principle of summation of rectilinear uniform movements. The aim of the work is to determine how things are in a similar situation when adding rotational synchronous movements. It was found that just as the result of the addition of two uniform rectilinear mechanical movements is also a uniform rectilinear movement, the result of the addition of two uniform unidirectional circular movements is also a uniform circular movement. The hodograph when two uniform oppositely directed circular motions are added is an ellipse. In a particular case, the ellipse can degenerate into a straight line segment. When two asynchronous rotations are added, hodographs in the form of a cochlea are possible, which is similar to Pascal's cochlea.

Applications: Gears, Ratios, And The Bicycle

1989 ◽  
Vol 82 (6) ◽  
pp. 466-468
Author(s):  
Daniel Timothy Gerber
Keyword(s):  
Applied Mathematics ◽  
Textbook Author ◽  
Mathematics Problems ◽  
Mathematics Course

Inevitably a teacher will encounter students who see “no reason” to study mathematics beyond the basics. When asked why they are enrolled in a higher mathematics course, students usually mention college requirements. It then becomes the responsibility of the textbook author and the instructor to generate interest in mathematics. Authors generally include applied mathematics problems in their texts; however, students find such problems more interesting when they can directly acquire the information needed for solution. This approach is certainly a teaching advantage if the instructor is willing to bring props into the classroom. In this spirit, I have used a ten-speed bicycle to illustrate gear function because it is familiar to most students.

scholarly journals Advanced Mesh-Based and Particle-Based Numerical Methods for Engineering and Applied Mathematics Problems

2017 ◽  
Vol 2017 ◽  
pp. 1-2 ◽  
Author(s):  
Cheng-Tang Wu ◽  
Lihua Wang ◽  
Bernard Bonello ◽  
Leevan Ling ◽  
Ninshu Ma ◽  
...  
Keyword(s):  
Numerical Methods ◽  
Applied Mathematics ◽  
Mathematics Problems

scholarly journals A Selection of Benchmark Problems in Solid Mechanics and Applied Mathematics

2020 ◽  
Author(s):  
Jörg Schröder ◽  
Thomas Wick ◽  
Stefanie Reese ◽  
Peter Wriggers ◽  
Ralf Müller ◽  
...  
Keyword(s):  
Solid Mechanics ◽  
Applied Mathematics ◽  
Benchmark Problems ◽  
Material Interfaces ◽  
German Research Foundation ◽  
Simulation Techniques ◽  
Classical Fields ◽  
Computational Solid Mechanics ◽  
Selection Of ◽  
Quantities Of Interest

Abstract In this contribution we provide benchmark problems in the field of computational solid mechanics. In detail, we address classical fields as elasticity, incompressibility, material interfaces, thin structures and plasticity at finite deformations. For this we describe explicit setups of the benchmarks and introduce the numerical schemes. For the computations the various participating groups use different (mixed) Galerkin finite element and isogeometric analysis formulations. Some programming codes are available open-source. The output is measured in terms of carefully designed quantities of interest that allow for a comparison of other models, discretizations, and implementations. Furthermore, computational robustness is shown in terms of mesh refinement studies. This paper presents benchmarks, which were developed within the Priority Programme of the German Research Foundation ‘SPP 1748 Reliable Simulation Techniques in Solid Mechanics—Development of Non-Standard Discretisation Methods, Mechanical and Mathematical Analysis’.

Molecular chain networks and strain energy functions in rubber elasticity

2019 ◽  
Vol 377 (2144) ◽  
pp. 20180067 ◽  
Author(s):  
Michael M. Carroll
Keyword(s):  
Strain Energy ◽  
Applied Mathematics ◽  
Rubber Elasticity ◽  
Theme Issue ◽  
Energy Functions ◽  
Approximate Inverse ◽  
The Mean ◽  
Strain Energy Functions ◽  
The Relationship ◽  
Selection Of

A relatively simple molecular–statistical model for rubber elasticity, similar to the Wang–Guth and the Arruda–Boyce (AB) models, is presented. Discussion of some approximate inverse Langevin functions leads to the selection of a new one as the most attractive balance between accuracy and simplicity. Use of this approximation with the AB model, in particular, yields the logarithmic strain energy introduced by Gent that exhibits limiting chain extensibility. A rather unusual facet of the relationship between the three strain energies is that the new one is the mean of the other two. This article is part of the theme issue ‘Rivlin's legacy in continuum mechanics and applied mathematics’.

Cognitive gadgets and cognitive priors

2019 ◽  
Vol 42 ◽  
Author(s):  
Gian Domenico Iannetti ◽  
Giorgio Vallortigara
Keyword(s):  
Cognitive Neuroscience ◽  
Selection Of

Abstract Some of the foundations of Heyes’ radical reasoning seem to be based on a fractional selection of available evidence. Using an ethological perspective, we argue against Heyes’ rapid dismissal of innate cognitive instincts. Heyes’ use of fMRI studies of literacy to claim that culture assembles pieces of mental technology seems an example of incorrect reverse inferences and overlap theories pervasive in cognitive neuroscience.

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